CHAPTER 11 • fell, but there was no increase in employment The Neo-Keynesian Model • rates fell, but there was no new investment

• Supply did not create its own demand (Say’s Law)

Sasan Fayazmanesh

Summary This chapter deals with the Keynesian (neo-Keynesian) model of the equilibrium output.

It covers: 1) the consumption function, including marginal propensity to consume; 2) function, including marginal propensity to save; 3) investment function; 4) government expenditure function; 4) function; and 5) equilibrium level of output.

It also covers the concept of Keynesian or “expenditure .”

Introduction to neo-Keynesian “Work is what I want, not charity. Neoclassicals’ laissez faire theories of the labor Who will help me get a and loanable funds market made no sense during the job? of 1929-1939. 7 years in Detroit, no , sent away. The theories and pictures did not match! Furnish best of references, phone . .”

1 Dorothea Lange's Migrant Mother Nipomo, California, March 1936.

See more images of the Great Depression

In The General Theory of Employment, Interest and Money (1936), Keynes challenged some aspects of these theories, as well as the Say’s Law.

See: General Theory

Keynes went on to develop new theories of:

1) How outpu t and employment are determined. 2) How is determined. 3) What is the role of money in the economy.

Soon after, however, Keynes’s ideas were simplified and incorporated into the neoclassical models.

This was the beginning of the “ ” or “ neo-Keynesian ” model.

2 These assumption also make output (GNP) and The Basic Neo-Keynesian Model disposable personal income equal :

We start with the GNP (Y) identity: NNI = Y – Depreciation – IBTs

Y = C + Ig + G + (X−M) PI = NNI + Transfer payments

DPI = PI – Direct taxes

Y = DPI

Simplifying assumptions Since 1) Economy is “closed”: No X − M Y= DPI = Consumption +

Y = C + Ig + G Then : 1) Y = C+S (income side) 2) Economy is “private”: No G 2) Y = C+ I (output side) Y = C + I g 1 and 2 imply: 3) There is no depreciation: 3) S = I Gross investment = Net investment Since C+S = C+ I Y= C + I

These assumption also make output (GNP) and Note: S = I is just an accounting identity. income (disposable personal income) equal : As we will see, S = I does not imply economic NNI = Y – Depreciation – IBTs stability, since I is actual investment (I a) as opposed to planned investment (I p): PI = NNI + Transfer payments Ia = Ip + ∆ Inventories DPI = PI – Direct taxes Stable economy implies:

∆ Inventories = 0 and

S = Ip

3 Consumption Function Consumption function C Keynes hypothesized that consumption spending is a function of disposable personal income: C=f(Y) C= f(Y).

This idea became known as the consumption function: a Def. Consumption function (C): a relationship between consumption spending and income Y (Income) (disposable personal income). -a

Shifts or Changes in Consumption After Keynes, it was argued that consumption depends on various other factors: If C = f (Y, W, i, E),

C = f (Y, W, i, E) then any change in W, i, or E will shift the consumption function. Where, Example, W: is wealth or assets, i: is interest rate, What happens if interest rates fall ? E: is expectation of future income.

Interest rates falls Keynes assumed : C

1) There is a minimum amount of consumption ; i.e., C1 = f (Y 0, W 0, i1, E 0 ) even when national income is zero, there is still some consumption. This is called autonomous consumption. C0 = f (Y 0, W 0, i0, E 0 ) a1

Q: Where could this consumption come from? a0 A: Past savings.

2) Consumption rises as national income rises , but it Y does not rise as fast.

4 Linear consumption function: MPC = ∆C/∆Y We assume that consumption function is given by : MPC = (C2 – C1) / (Y2 – Y1) C = a + bY MPC = ($1000 – $850) / ($1200 – $1000) Where “ a” is the C intercept and “ b” is the slope of the MPC = $150/ $200 consumption function. MPC = 3/4 = .75 It must be that:

0 < b < 1

Marginal Propensity to Consume Average Propensity to Consume

Def. Marginal Propensity to Consume (MPC) : The Def. Average Propensity to Consume (APC) : increase in consumption which results from an increase in income: The level of consumption divided by the level of income:

MPC = ∆C/ ∆Y APC = C / Y

This is obviously the same as the slope of the APC obviously changes as income changes. consumption function or “ b”:

MPC = b

Example Example C C

C= a + by C= a + bY

C2=$1000 C2=$1000

C1=$850 C1=$850

Y Y

Y1 = $1000 Y 2= $1200 Y1 = $1000 Y 2= $1200

5 Marginal Propensity to Save

APC 1 = C 1/Y 1 Def. Marginal Propensity to Save (MPS) : The increase in saving which results from an increase in income: APC 1 = $850/$1000 MPS = ∆S/ ∆Y APC 1 = .85 This is the same as the slope of the savings function or “1− b” APC 2 = C 2/Y 2 MPS = 1 − b APC 2 = $1000/ $1200

APC 2 = .83333

Saving Function Example C Y = S +C, Therefore,

S = Y− C C= a + bY

C2=$1000 If C = a + bY, then C =$850 1 S = − a + (1 − b) Y S = Y − ( a + bY)

S2=$200 S = Y − a − bY S1 =$150 Y S = − a + (1 − b) Y Y1 = $1000 Y 2= $1200

Saving function MPS = ∆S/∆Y C, S MPS = (S2 – S1) / (Y2 – Y1)

C = a +bY MPS = ($200 – $150) / ($1200 – $1000)

MPS = $50/ $200 a S = − a + (1 − b) Y MPS = 1/4 = .25

Y

-a

6 Q: What do we get when we add MPC and MPS? Q: What do we get when we add APC and APS?

A: One! A: One, again!

Our example: Our example:

MPC =.75 APC =.85 MPS =.25 APS =.15

MPC +MPS =.75 +.25 = 1 APC +APS =.85 +.15 = 1

MPC + MPS = 1 is true by definition: APC +APS = 1 is also true by definition:

MPC = b Y = C +S MPS = 1-b MPC +MPS =b + 1- b = 1 Divide both sides by Y:

Y/Y = C/Y + S/Y

1 = APC +APS

Similarly Investment Function

Y= C +S Remember that actual investment (I) has 3 components:

∆ Y= ∆ C + ∆ S 1) Structures and equipment 2) Residential structures Divide both sides by ∆ Y 3) Changes in inventories

∆ Y/ ∆ Y = ∆ C/ ∆ Y + ∆ S / ∆ Y

1 = MPC + MPS

7 Also remember the relation between actual investment Equilibrium Level of GNP (Y) (I a ) and planned investment (I p): Q: At what level of consumption, saving and investment Ia = I p + ∆ Inventories will the GNP be in equilibrium, i.e., it is neither expanding nor contracting? Def. Planned investment (Ip ) is what firms wish or plan to invest. A: We can answer this question in 2 ways:

1) By looking at the relationship between savings and investment, or

2) By looking at the relation between expenditures (C and I) and national income.

Keynes assumed that planned investment : Savings and Investment: Equilibrium level of GNP

1) Is independent of the level of national S, I S ≡ I income. a

2) Depends on interest rate , as we shall see later.

IP

Y Ye ∆ Inventories= 0

Planned investment function Savings and Investment: Equilibrium level of GNP

Investment (I) S, I S ≡ I a

∆ I> 0

IP IP

Y Y Ye Y1 ∆ I= 0 ∆ I> 0

8 Savings and Investment: Equilibrium level of GDP Aggregate Expenditure

S, I AE (C, I) S ≡ I a

AE = C+ I p

Ip C Ip IP ∆ I< 0 Ip

Y Y Y2 Ye ∆ I< 0

The 45 0 line Aggregate Expenditure AE (C, I) We can also look at the level of equilibrium GDP by AE = Y looking at where aggregate expenditure is equal to income. AE 2

AE 1 Def. Aggregate Expenditure (AE ): Is the sum of the spending. So far we have:

AE = C+I 45 0 Y

Y1 Y2

Aggregate Expenditure Equilibrium level of GDP

AE (C, I) AE (C, I) AE = Y

AE = C + I p

AE e C

Ip 45 0 Y Y

Ye “Keynesian Cross”

9 Note: At equilibrium level of output, Ye, all Government expenditure income is spent. Suppose the equilibrium level of output is achieved Economy is neither expanding not contacting. at a low level of employment.

It is stable and ∆I = 0 . then advocates government spending money on and services.

We assume that government expenditure, G, is independent of national income:

Equilibrium level of GDP Government expenditure function

AE (C, I) AE = Y Government expenditure (G)

∆ I> 0 AE = C + I p AE e ∆ I< 0 G

45 0 Y Y

Y2 Ye Y1

Equilibrium level of GNP: Everything together Aggregate Expenditure Again AE = Y S, I, C AE (C, I)

AE = C+ I p

S C + I IP G 45 0 Y Y Ye ∆ I= 0

10 Aggregate Expenditure The Multiplier Effect

Def. Multiplier Effect : Any change in spending AE (C, I, G) will bring about greater change in income or output:

AE = C+ I + G ∆Y > ∆AE G C + I G G

Y

Equilibrium level of GNP again A Numerical Example

AE = Y Suppose MPC=1/2 and investment increases by AE (C, I, G) $1000 , i.e., ∆I = $1000 .

AE 1 = C+ I+ G What happens to he national income? AE 0 = C+ I ∆AE = G

45 0 Y

Y0 Y1

Note: ∆Y > ∆AE Period 1: ∆∆∆I=$1000 ∆Y=$1000 AE = Y AE (C, I, G) Period 2 ∆C=$500 ∆S=$500

AE 1 = C+ I+ G

AE 0 = C+ I ∆AE = G

45 0 ∆Y Y

Y0 Y1

11 Period 1: ∆∆∆I=$1000 ∆Y=$1000 Remember the geometric series:

Period 2 ∆C=$500 $500 ∆S=$500 S= a+ ar +ar 2+ ar 3 +ar 4+ . . .

Period 3 $250 $250 Where 0 < r <1

The series converges: S = a/(1− r)

∆∆∆ ∆ Period 1: I=$1000 Y=$1000 Net Result: ∆ ∆ Period 2 C=$500 $500 S=$500 ∆Y = $1000+ $500+ $250+ $125 + $62.5 + . . .

Period 3 $250 $250 $250 ∆Y = $1000+ $1000 (1/2)+ $1000 (1/2)2 + . . .

∆Y = $1000/(1-1/2) = $1000/(1/2) = 2 x $1000

∆Y = $2, 000

Algebraic method of calculating multiplier Period 1: ∆∆∆I=$1000 ∆Y=$1000

Period 2 ∆C=$500 $500 ∆S=$500 ∆Y = ∆AE / (1-MPC) = ∆AE / (MPS) Period 3 $250 $250 $250 We call k = 1 = 1 Period 4 $125 $125 $125 1-MPC MPS Period 5 $62.5 $62.5 $62.5 the multiplier factor , Keynesian or expenditure multiplier......

∆∆∆C=$1000 ∆∆∆Y=$2000 ∆∆∆S=$1000

12 Proof (not required) Does the multiplier work in reality?

1) Y= C+I Some Keynesians argue that “ automatic stabilizers ” might hinder the effectiveness of multiplier. 2) ∆Y = ∆C+ ∆ I Def. Automatic stabilizers are economics 3) ∆Y− ∆C = ∆I (divide both sides by ∆Y ) forces that try to stabilize economy automatically.

4) ( ∆Y− ∆C) / ∆Y= ∆I / ∆Y

5) 1−MPC = ∆I / ∆Y

6) ∆Y = ∆ I /(1−MPC)

Our previous example : Examples of automatic stabilizers

Investment increased by $1000 and MPC= 1/2.  Progressive income tax : as income goes up, By how much will national income rise? people fall in higher marginal tax rate. ∆ ∆ Y = AE / (1−MPC)  : as economy expands, rises, reducing spending. ∆Y = ∆I / (1 − MPC)  Interest rate : also, as economy expands , interest ∆ Y = $1000/ (1 − 1/2) rates rise, slowing expenditures. ∆Y = $1000/ (1/2)

∆Y = $2000

Another example of multiplier: Note: Consumption depends on disposal income; that is, if T stands for taxes, then: Suppose government expenditure, G, falls by $150 and MPC = 2/3. By how much will national income fall? C= a + b (Y ‒T) ∆Y = ∆AE / (1−MPC) C= a ‒ bT + bY

∆Y = ∆G / (1 − MPC) Thus reducing taxes will also increase consumption and GDP. ∆Y = − $150/ (1 − 2/3) But tax reduction will have less impact on GDP than ∆Y = − $150/ (1/3) an increase in government spending.

∆Y = − $450

13 Indeed, if government increases its expenditures by the same amount as it raises taxes, GDP will still grow by the amount of government expenditures:

T=G The result of tax increase: C= a + bY C= a + b (Y ‒T) C= a ‒ bT + bY ∆ C = ‒ bT ∆Y = ∆ C / (1 − b) = ‒ bT/ (1 − b) = ‒ b G/ (1 − b)

The result of expenditure increase: ∆ Y = G / (1 − b)

If we add the two results we get a balanced budget multiplier of 1:

∆Y = [G / (1 − b)] ‒ [b G/ (1 − b)] ∆Y = G (1 − b)/(1 − b) ∆Y = G (1 − b)/(1 − b) ∆Y = G

Next stop: Chapter 13.

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